已知cos2a=3/5,求sin^4*a+cos^4*a=?

cos2a=3/5
(sin2a)^2= (1-(cos2a)^2 = 16/25
cos^2a - sin^2a = 3/5
(cos^2a - sin^2a )^2 = 9/25
(cos^2a - sin^2a )^2 = 9/25
sin^4*a+cos^4*a-2(sinacosa)^2 = 9/25
sin^4*a+cos^4*a-1/2(sin2a)^2 = 9/25
sin^4*a+cos^4*a = 9/25+1/2(sin2a)^2=9/25+1/2*16/25=17/25

cos2α=cosα²-sinα²
cos²2α=(cosα²-sinα²)²=sin^4*α+cos^4*α-2sin²αcos²α
=sin^4*α+cos^4*α-sin²2α
所以cos²2α=sin^4*α+cos^4*α-sin²2α
cos²2α=9/25 sin²2α=16/25
sin^4*α+cos^4*α=1